Triple divisor type functions in arithmetic progressions to prime power moduli

Abstract

We study the equidistribution in arithmetic progressions modulo powers of a fixed odd prime of Hecke eigenvalues of noncuspidal ${\mathrm{GL}}_3$ automorphic forms, with a focus on the convolution coefficients ${\lambda }_{1⊞f}(n)=({\lambda }_f\star 1)(n)$,attached to a level $1$ holomorphic primitive cusp form $f$. Utilizing techniques introduced by Kowalski--Lin--Michel and Milićević, we prove the exponent $\vartheta =1/2+7/458-\epsilon$ is admissible.

16 pages